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Tutorial 1 Ata Kaban A.Kaban@cs.bham.ac.uk http://www.cs.bham.ac.uk/~axk School of Computer Science University of Birmingham

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Iterated Prisoner's Dilemma Invented by Merrill Flood & Melvin Dresher in 1950s Studied in game theory, economics, political science The story –Alice and Bob arrested, no communication between them –They are offered a deal: If any of them confesses & testifies against the other then gets suspended sentence while the other gets 5 years in prison If both confess & testify against the other, they both get 4 years If none of them confesses then they both get 2 years –What is the best strategy for maximising one’s own payoff?

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Abstract formulation through a payoff matrix Player A Player B CooperateDefect Cooperate3,30,5 Defect5,01,1

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2 tournaments – participants have sent strategies Human strategies played against each other Winner: TIT FOR TAT –Cooperates as long the other player does not defect –Defects on defection until the other player begins to cooperate again Can GA evolve a better strategy?

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Individuals = strategies How to encode a strategy by a string? Let memory depth of previous moves=1 Fix a canonical order of cases: AB –Case 1:CC –Case 2:CD –Case 3:DC –Case 4:DD e.g. strategy encoding (for A): ‘CDCD’

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Now let memory dept of previous moves=3 –How many cases? ……… Case 1: …….. Case 2: …….. … –How many letters are needed to encode a strategy as a string? …………… –How many strategies there are? …………. Is that a large number?

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Experiment 1 –40 runs with different random initialisations –50 generations each –Population of 20 –Fitness=avg score over all games played –A fixed environment of 8 human-designed strategies Results –Found better strategy than those 8 strategies in the environment! –Even though – how many strategies were only tested in a run out of all possible strategies? …………… –What does this result mean? …………….

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Experiment 2 –changing environment: the evolving strategies played against each other. Results – Found strategies similar in essence with the winner human-designed strategy Idealised model of evolution & co-evolution

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When to use Evolutionary Algorithms? The space to be searched is large –What if it is not? The space to be searched is known not to be perfectly smooth and unimodal –Otherwise? The search space is not well understood –If it is? Quickly finding a sufficiently good solution is enough Noisy data –Think about it, why?

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APEC 8205: Applied Game Theory Fall 2007

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